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There are two major ways of encoding a neural network into a chromosome, as required in design of a genetic algorithm (GA). These are explicit (direct) and implicit (indirect) encoding methods. The proposed direct encoding method to design higher order neural networks (HONN) does not use any known learning algorithm - rather it uses a gradient descent method to minimize the mean output error. The simple feed-forward network only uses one pass, called forward pass contrary to the standard learning algorithm which does the training in two passes. This saves an enormous amount of training time and the network converges to an optimum value as compared to other learning strategies.